Research methodology

2020 ◽  
pp. 381-392
Author(s):  
Robert D. Gibbons
Keyword(s):  
Longitudinal Data ◽  
Research Methodology ◽  
Computerized Adaptive Testing ◽  
Psychiatric Research ◽  
Physical Sciences ◽  
Variance Functions ◽  
Scale Models ◽  
Mean And Variance ◽  
The Mean ◽  
Data Location

Given the diversity of psychiatric research, having a statistically rigorous set of methodological tools for the design and analysis is critically important. The field of psychiatry has, in and of itself, inspired several advances in research methodology that have led to widespread use across all areas of medicine and, more generally, throughout the biological, social, and physical sciences. This chapter reviews statistical and methodological contributions to the analysis of longitudinal data, inter-rater agreement, item response theory (IRT), and computerized adaptive testing (CAT), as well as the joint modelling of both the mean and variance functions in intensive longitudinal data (location-scale models). It is written for a general psychiatric research audience, but lays out areas for future study and development for quantitative scientists as well.

scholarly journals EVALUASI NUMERIK PENDUGA FUNGSI NILAI HARAPAN DAN FUNGSI RAGAM PROSES POISSON MAJEMUK DENGAN INTENSITAS EKSPONENSIAL FUNGSI LINEAR

2018 ◽  
Vol 17 (2) ◽  
pp. 157
Author(s):  
S. UTAMI ◽  
I W. MANGKU ◽  
I G. P. PURNABA
Keyword(s):  
Monte Carlo ◽  
Confidence Intervals ◽  
Observation Interval ◽  
Compound Poisson Process ◽  
Intensity Function ◽  
Significance Level ◽  
Variance Functions ◽  
Mean And Variance ◽  
The Mean ◽  
Strongly Consistent

<em>Performances of estimators for the mean and variance functions of a compound Poisson process having intensity obtained as an exponential of linear function are investigated using Monte Carlo simulations. The intensity function of this process is assumed to be </em>𝑒𝑥𝑝(𝛼+𝛽𝑠) <em>with </em>0&lt;𝛽&lt;<em>∞</em>, <em>where </em>𝛽 <em>is assumed to be known. In [8], estimators of the mean and variance functions of this process have been constructed and have been proved to be unbiased, weakly and strongly consistent. The objectives of this research are to check distributions of these estimators using Monte Carlo simulation and to check the convergence to </em>1−𝛼 <em>of the probabilities that the parameters are contained in the confidence intervals constructed in [11]. Results of the research are as follows. Distribution of estimators for the mean and variance functions are approximately normal. For a given significance level </em>𝛼<em>, the larger the size of observation interval, the closer the probabilities that the parameters are contained in the confidence intervals to </em>1−𝛼<em>.</em>

scholarly journals Semiparametric Smoothing Spline in Joint Mean and Dispersion Models with Responses from the Biparametric Exponential Family: A Bayesian Perspective

2021 ◽  
Vol 9 (2) ◽  
pp. 351-367
Author(s):  
Héctor Zárate ◽  
Edilberto Cepeda
Keyword(s):  
Exponential Family ◽  
Parametric Models ◽  
Efficient Estimation ◽  
Smoothing Methods ◽  
Markov Chain Sampling ◽  
Variance Functions ◽  
Natural Connection ◽  
Mean And Variance ◽  
The Mean ◽  
Two Parameter

This article extends the fusion among various statistical methods to estimate the mean and variance functions in heteroscedastic semiparametric models when the response variable comes from a two-parameter exponential family distribution. We rely on the natural connection among smoothing methods that use basis functions with penalization, mixed models and a Bayesian Markov Chain sampling simulation methodology. The significance and implications of our strategy lies in its potential to contribute to a simple and unified computational methodology that takes into account the factors that affect the variability in the responses, which in turn is important for an efficient estimation and correct inference of mean parameters without the requirement of fully parametric models. An extensive simulation study investigates the performance of the estimates. Finally, an application using the Light Detection and Ranging technique, LIDAR, data highlights the merits of our approach.

First-order stochastic chemical reactions and oscillations in the variance

1980 ◽  
Vol 17 (04) ◽  
pp. 1087-1093 ◽  
Author(s):  
Richard C. Hertzberg ◽  
Vincent F. Gallucci
Keyword(s):  
General Solution ◽  
Markov Model ◽  
Random Processes ◽  
Numerical Examples ◽  
First Order ◽  
Variance Functions ◽  
First Order Kinetics ◽  
Component Systems ◽  
Mean And Variance ◽  
The Mean

The general solution of a Markov model for first-order kinetics is developed as a sum of independent, multinomially distributed random processes. Fluctuations in the mean and variance functions are discussed and shown to be unrelated in time during the early phase of the reaction. Numerical examples are presented for two- and three-component systems.

SIMULTANEOUS SPECIFICATION TESTING OF MEAN AND VARIANCE STRUCTURES IN NONLINEAR TIME SERIES REGRESSION

2011 ◽  
Vol 27 (4) ◽  
pp. 792-843 ◽  
Author(s):  
Song Xi Chen ◽  
Jiti Gao
Keyword(s):  
Time Series ◽  
Empirical Likelihood ◽  
Goodness Of Fit ◽  
Test Procedure ◽  
Single Pair ◽  
Test Statistic ◽  
Time Series Regression ◽  
Variance Functions ◽  
Mean And Variance ◽  
The Mean

This paper proposes a nonparametric simultaneous test for parametric specification of the conditional mean and variance functions in a time series regression model. The test is based on an empirical likelihood (EL) statistic that measures the goodness of fit between the parametric estimates and the nonparametric kernel estimates of the mean and variance functions. A unique feature of the test is its ability to distribute natural weights automatically between the mean and the variance components of the goodness-of-fit measure. To reduce the dependence of the test on a single pair of smoothing bandwidths, we construct an adaptive test by maximizing a standardized version of the empirical likelihood test statistic over a set of smoothing bandwidths. The test procedure is based on a bootstrap calibration to the distribution of the empirical likelihood test statistic. We demonstrate that the empirical likelihood test is able to distinguish local alternatives that are different from the null hypothesis at an optimal rate.

First-order stochastic chemical reactions and oscillations in the variance

1980 ◽  
Vol 17 (4) ◽  
pp. 1087-1093 ◽  
Author(s):  
Richard C. Hertzberg ◽  
Vincent F. Gallucci
Keyword(s):  
General Solution ◽  
Markov Model ◽  
Random Processes ◽  
Numerical Examples ◽  
First Order ◽  
Variance Functions ◽  
First Order Kinetics ◽  
Component Systems ◽  
Mean And Variance ◽  
The Mean

The general solution of a Markov model for first-order kinetics is developed as a sum of independent, multinomially distributed random processes. Fluctuations in the mean and variance functions are discussed and shown to be unrelated in time during the early phase of the reaction. Numerical examples are presented for two- and three-component systems.

scholarly journals A flexible model for the mean and variance functions, with application to medical cost data

2013 ◽  
Vol 32 (24) ◽  
pp. 4306-4318 ◽  
Author(s):  
Jinsong Chen ◽  
Lei Liu ◽  
Daowen Zhang ◽  
Ya-Chen T. Shih
Keyword(s):  
Medical Cost ◽  
Cost Data ◽  
Variance Functions ◽  
Medical Cost Data ◽  
Mean And Variance ◽  
The Mean ◽  
Flexible Model

scholarly journals Weighted statistical binary patterns for facial feature representation

2021 ◽  
Author(s):  
Hung Phuoc Truong ◽  
Thanh Phuong Nguyen ◽  
Yong-Guk Kim
Keyword(s):  
Comprehensive Evaluation ◽  
Facial Feature ◽  
Input Image ◽  
Feature Representation ◽  
Illumination Variation ◽  
Straight Line ◽  
Mean And Variance ◽  
The Mean ◽  
Face Datasets ◽  
Degraded Images

AbstractWe present a novel framework for efficient and robust facial feature representation based upon Local Binary Pattern (LBP), called Weighted Statistical Binary Pattern, wherein the descriptors utilize the straight-line topology along with different directions. The input image is initially divided into mean and variance moments. A new variance moment, which contains distinctive facial features, is prepared by extracting root k-th. Then, when Sign and Magnitude components along four different directions using the mean moment are constructed, a weighting approach according to the new variance is applied to each component. Finally, the weighted histograms of Sign and Magnitude components are concatenated to build a novel histogram of Complementary LBP along with different directions. A comprehensive evaluation using six public face datasets suggests that the present framework outperforms the state-of-the-art methods and achieves 98.51% for ORL, 98.72% for YALE, 98.83% for Caltech, 99.52% for AR, 94.78% for FERET, and 99.07% for KDEF in terms of accuracy, respectively. The influence of color spaces and the issue of degraded images are also analyzed with our descriptors. Such a result with theoretical underpinning confirms that our descriptors are robust against noise, illumination variation, diverse facial expressions, and head poses.

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